Cahiers du CEREMADE 

Unité
Mixte de Recherche du C.N.R.S. N°7534 

Abstract : In this paper we consider a new approach for single object
segmentation in 3D images. Our model finds a surface that has two
curves as boundary conditions and that minimizes the integral of a
potential function that corresponds to the image features. These given
curves are supposed to belong to the surface to extract and thus,
constitute user given information. Our goal is achieved by building
globally minimal paths between points located on each curve. To that
end, we give some mathematical results on the equation satisfied by
these paths and the link with the Eikonal equation. We then
approximate the surface to extract by a discrete network of these
paths. Furthermore, an interpolation method is used to build a mesh
or an implicit representation based on the information retrieved from
the network. Our paper describes a fast construction obtained by
exploiting the Fast Marching algorithm and a fast analytical
interpolation method. Moreover, a Level set method can be used to
refine the segmentation when higher accuracy is required. The
algorithm has been successfully applied to 3D medical images and
synthetic images. 





200534 

07072005 

Université
de PARIS  DAUPHINE Place du Maréchal de Lattre De Tassigny  75775 PARIS CEDEX 16  FRANCE Téléphone : +33 (0)1 44054923  fax : +33 (0)1 44054599 